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Write the first paragraph of your page here. Section heading Write the first section of your page here. I.R.T Item Response Theory is the study of test and item scores based on assumptions concerning the mathematical relationship between abilities (or other hypothesized traits) and item responses. Other names and subsets include Item Characteristic Curve Theory, Latent Trait Theory, Rasch Model, 2PL Model, 3PL model and the Birnbaum model. Item Response Theory is also sometimes called latent trait theory. This is a modern test theory (as opposed to classical test theory). It is not the only modern test theory, but it is the most popular one and is currently an area of active research. IRT requires stronger assumptions than classical test theory (we will cover these in a moment). IRT is much intuitive approach to measurement once you get used to it. In IRT, the true score is defined on the latent trait of interest rather than on the test, as is the case in classical test theory. IRT is popular because it provides a theoretical justification for doing lots of things that classical test theory does not. Some applications where IRT is handy include: *Item bias analysis--IRT provides a test of item equivalence across groups. We can test whether an item is behaving differently for blacks and whites or for males and females, for example. The same logic can be applied to translations of attitude scales into different languages. We can test whether the item means the same thing in English and French, for example. *Equating--Sometimes we have scores on one test and we would like to know what the equivalent score would be on another test (e.g., versions or forms of the SAT). IRT provides a theoretical justification for equating scores from one test to another. *Tailored Testing--IRT provides an estimate of the true score that is not based on the number of correct items. This frees us to give different people different test items but still place people on the same scale. One particularly exciting feature of tailored testing is the capability to give people test items that are matched (close) to them. A tailored testing program for the SAT will give more difficult items to brighter test takers. This also has implications for test security -- different people get different tests. The concept of the item response function was around before 1950. The pioneering work of IRT as a theory occurred during the 1950s and 1960s. Three of the pioneers were the Educational Testing Service psychometrician Frederic M. Lord,[2] the Danish mathematician Georg Rasch, and Austrian sociologist Paul Lazarsfeld, who pursued parallel research independently. Key figures who furthered the progress of IRT include Benjamin Drake Wright and David Andrich. IRT did not become widely used until the late 1970s and 1980s, when personal computers gave many researchers access to the computing power necessary for IRT. Among other things, the purpose of IRT is to provide a framework for evaluating how well assessments work, and how well individual items on assessments work. The most common application of IRT is in education, where psychometricians use it for developing and refining exams, maintaining banks of items for exams, and equating for the difficulties of successive versions of exams (for example, to allow comparisons between results over time).[3] IRT models are often referred to as latent trait models. The term latent is used to emphasize that discrete item responses are taken to be observable manifestations of hypothesized traits, constructs, or attributes, not directly observed, but which must be inferred from the manifest responses. Latent trait models were developed in the field of sociology, but are virtually identical to IRT models. IRT is generally regarded as an improvement over classical test theory (CTT). For tasks that can be accomplished using CTT, IRT generally brings greater flexibility and provides more sophisticated information. Some applications, such as computerized adaptive testing, are enabled by IRT and cannot reasonably be performed using only classical test theory. Another advantage of IRT over CTT is that the more sophisticated information IRT provides allows a researcher to improve the reliability of an assessment. IRT entails three assumptions: #A unidimensional trait denoted by ; #Local independence of items; #The response of a person to an item can be modeled by a mathematical item response function (IRF). The trait is further assumed to be measurable on a scale (the mere existence of a test assumes this), typically set to a standard scale with a mean of 0.0 and a standard deviation of 1.0. 'Local independence' means that items are not related except for the fact that they measure the same trait, which is equivalent to the assumption of unidimensionality, but presented separately because multidimensionality can be caused by other issues. The topic of dimensionality is often investigated with factor analysis, while the IRF is the basic building block of IRT and is the center of much of the research and literature.